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For the function f(x) = x^(x), find the ...

For the function `f(x) = x^(x)`, find the points at which it is (i) increasing and (ii) decreasing. Hence determine which of `e^(pi), pi^(e)` is greater.

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The correct Answer is:
f, is strictly decreasing on it is strictly increasing on `(1//e)`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-APPLICATION OF DERIVATIVES-Exercise-10(h)
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  3. Find the points of local extrema (if any) and local extrema of the fol...

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  4. Find the points at which the functions f(x) = x^(3) - 6x^(2) + 9x + ...

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  5. Find the points of local extrema (if any) and local extrema of the fol...

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  6. Find the points of local extrema (if any) and local extrema of the fol...

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  7. Find the points of local extrema (if any) and local extrema of the fol...

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  8. Find the points of local extrema (if any) and local extrema of the fol...

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  9. Find the points of local extrema (if any) and local extrema of the fol...

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  10. Find the points of local extrema (if any) and local extrema of the fol...

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  11. Find the points of local extrema (if any) and local extrema of the fol...

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  12. Prove that the functions do not have maxima or minima: f(x) = e^(x)

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  13. Prove that the functions do not have maxima or minima: g(x) = log ...

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  14. Prove that the following functions do not have absolute maximum and ab...

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  15. Find the absolute maximum value and the absolute minimum value of the ...

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  16. Find the absolute maximum value and the absolute minimum value of the ...

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  17. Find the absolute maximum value and absolute minimum value of the foll...

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  18. Find the absolute maximum value and the absolute minimum value of the ...

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  19. Find the absolute maximum value and absolute minimum value of the foll...

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  20. Use the first derivative test to find the local extrema of f(x) =x^(3)...

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  21. Use the first derivative test to find local extrema of f(x) = x^(2) - ...

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